docs: def execute(self, style, xpoints, ypoints, zpoints, mask=None,
                  backend='vectorized', specified_drift_arrays=None):
          """Calculates a kriged grid and the associated variance.
  
          This is now the method that performs the main kriging calculation.
          Note that currently measurements (i.e., z values) are
          considered 'exact'. This means that, when a specified coordinate for
          interpolation is exactly the same as one of the data points,
          the variogram evaluated at the point is forced to be zero. Also, the
          diagonal of the kriging matrix is also always forced to be zero.
          In forcing the variogram evaluated at data points to be zero, we are
          effectively saying that there is no variance at that point
          (no uncertainty, so the value is 'exact').
  
          In the future, the code may include an extra 'exact_values' boolean
          flag that can be adjusted to specify whether to treat the measurements
          as 'exact'. Setting the flag to false would indicate that the variogram
          should not be forced to be zero at zero distance (i.e., when evaluated
          at data points). Instead, the uncertainty in the point will be equal
          to the nugget. This would mean that the diagonal of the kriging matrix
          would be set to the nugget instead of to zero.
  
          Parameters
          ----------
          style : str
              Specifies how to treat input kriging points. Specifying 'grid'
              treats xpoints, ypoints, and zpoints as arrays of x, y, and z
              coordinates that define a rectangular grid. Specifying 'points'
              treats xpoints, ypoints, and zpoints as arrays that provide
              coordinates at which to solve the kriging system. Specifying
              'masked' treats xpoints, ypoints, and zpoints as arrays of x, y,
              and z coordinates that define a rectangular grid and uses mask
              to only evaluate specific points in the grid.
          xpoints : array_like, shape (N,) or (N, 1)
              If style is specific as 'grid' or 'masked', x-coordinates of
              LxMxN grid. If style is specified as 'points', x-coordinates of
              specific points at which to solve kriging system.
          ypoints : array_like, shape (M,) or (M, 1)
              If style is specified as 'grid' or 'masked', y-coordinates of
              LxMxN grid. If style is specified as 'points', y-coordinates of
              specific points at which to solve kriging system. Note that in this
              case, xpoints, ypoints, and zpoints must have the same dimensions
              (i.e., L = M = N).
          zpoints : array_like, shape (L,) or (L, 1)
              If style is specified as 'grid' or 'masked', z-coordinates of
              LxMxN grid. If style is specified as 'points', z-coordinates of
              specific points at which to solve kriging system. Note that in this
              case, xpoints, ypoints, and zpoints must have the same dimensions
              (i.e., L = M = N).
          mask : boolean array, shape (L, M, N), optional
              Specifies the points in the rectangular grid defined by xpoints,
              ypoints, zpoints that are to be excluded in the kriging
              calculations. Must be provided if style is specified as 'masked'.
              False indicates that the point should not be masked, so the kriging
              system will be solved at the point.
              True indicates that the point should be masked, so the kriging
              system will not be solved at the point.
          backend : string, optional
              Specifies which approach to use in kriging. Specifying 'vectorized'
              will solve the entire kriging problem at once in a vectorized
              operation. This approach is faster but also can consume a
              significant amount of memory for large grids and/or large datasets.
              Specifying 'loop' will loop through each point at which the kriging
              system is to be solved. This approach is slower but also less
              memory-intensive. Default is 'vectorized'.
          specified_drift_arrays : list of array-like objects, optional
              Specifies the drift values at the points at which the kriging
              system is to be evaluated. Required if 'specified' drift provided
              in the list of drift terms when instantiating the UniversalKriging3D
              class. Must be a list of arrays in the same order as the list
              provided when instantiating the kriging object. Array(s) must be
              the same dimension as the specified grid or have the same number
              of points as the specified points; i.e., the arrays either must be
              shape (L, M, N), where L is the number of z grid-points,
              M is the number of y grid-points, and N is the number of
              x grid-points, or shape (N,) or (N, 1), where N is the number of
              points at which to evaluate the kriging system.
  
          Returns
          -------
          kvalues : ndarray, shape (L, M, N) or (N,) or (N, 1)
              Interpolated values of specified grid or at the specified set
              of points. If style was specified as 'masked', kvalues will be a
              numpy masked array.
          sigmasq : ndarray, shape (L, M, N) or (N,) or (N, 1)
              Variance at specified grid points or at the specified set of points.
              If style was specified as 'masked', sigmasq will be a numpy
              masked array.
          """
  
          if self.verbose:
              print("Executing Ordinary Kriging...\n")
  
          if style != 'grid' and style != 'masked' and style != 'points':
              raise ValueError("style argument must be 'grid', 'points', "
                               "or 'masked'")
  
          xpts = np.atleast_1d(np.squeeze(np.array(xpoints, copy=True)))
          ypts = np.atleast_1d(np.squeeze(np.array(ypoints, copy=True)))
          zpts = np.atleast_1d(np.squeeze(np.array(zpoints, copy=True)))
          n = self.X_ADJUSTED.shape[0]
          n_withdrifts = n
          if self.regional_linear_drift:
              n_withdrifts += 3
          if self.specified_drift:
              n_withdrifts += len(self.specified_drift_data_arrays)
          if self.functional_drift:
              n_withdrifts += len(self.functional_drift_terms)
          nx = xpts.size
          ny = ypts.size
          nz = zpts.size
          a = self._get_kriging_matrix(n, n_withdrifts)
  
          if style in ['grid', 'masked']:
              if style == 'masked':
                  if mask is None:
                      raise IOError("Must specify boolean masking array "
                                    "when style is 'masked'.")
                  if mask.ndim != 3:
                      raise ValueError("Mask is not three-dimensional.")
                  if mask.shape[0] != nz or mask.shape[1] != ny or mask.shape[2] != nx:
                      if mask.shape[0] == nx and mask.shape[2] == nz and mask.shape[1] == ny:
                          mask = mask.swapaxes(0, 2)
                      else:
                          raise ValueError("Mask dimensions do not match "
                                           "specified grid dimensions.")
                  mask = mask.flatten()
              npt = nz * ny * nx
              grid_z, grid_y, grid_x = np.meshgrid(zpts, ypts, xpts, indexing='ij')
              xpts = grid_x.flatten()
              ypts = grid_y.flatten()
              zpts = grid_z.flatten()
          elif style == 'points':
              if xpts.size != ypts.size and ypts.size != zpts.size:
                  raise ValueError("xpoints and ypoints must have same "
                                   "dimensions when treated as listing "
                                   "discrete points.")
              npt = nx
          else:
              raise ValueError("style argument must be 'grid', 'points', "
                               "or 'masked'")
  
          if specified_drift_arrays is None:
              specified_drift_arrays = []
          spec_drift_grids = []
          if self.specified_drift:
              if len(specified_drift_arrays) == 0:
                  raise ValueError("Must provide drift values for kriging "
                                   "points when using 'specified' drift "
                                   "capability.")
              if type(specified_drift_arrays) is not list:
                  raise TypeError("Arrays for specified drift terms must "
                                  "be encapsulated in a list.")
              for spec in specified_drift_arrays:
                  if style in ['grid', 'masked']:
                      if spec.ndim < 3:
                          raise ValueError("Dimensions of drift values array do "
                                           "not match specified grid dimensions.")
                      elif spec.shape[0] != nz or spec.shape[1] != ny or spec.shape[2] != nx:
                          if spec.shape[0] == nx and spec.shape[2] == nz and spec.shape[1] == ny:
                              spec_drift_grids.append(np.squeeze(spec.swapaxes(0, 2)))
                          else:
                              raise ValueError("Dimensions of drift values array "
                                               "do not match specified grid "
                                               "dimensions.")
                      else:
                          spec_drift_grids.append(np.squeeze(spec))
                  elif style == 'points':
                      if spec.ndim != 1:
                          raise ValueError("Dimensions of drift values array do "
                                           "not match specified grid dimensions.")
                      elif spec.shape[0] != xpts.size:
                          raise ValueError("Number of supplied drift values in "
                                           "array do not match specified number "
                                           "of kriging points.")
                      else:
                          spec_drift_grids.append(np.squeeze(spec))
              if len(spec_drift_grids) != len(self.specified_drift_data_arrays):
                  raise ValueError("Inconsistent number of specified "
                                   "drift terms supplied.")
          else:
              if len(specified_drift_arrays) != 0:
                  warnings.warn("Provided specified drift values, but "
                                "'specified' drift was not initialized during "
                                "instantiation of UniversalKriging3D class.",
                                RuntimeWarning)
  
          xpts, ypts, zpts = _adjust_for_anisotropy(np.vstack((xpts, ypts, zpts)).T,
                                                    [self.XCENTER, self.YCENTER, self.ZCENTER],
                                                    [self.anisotropy_scaling_y, self.anisotropy_scaling_z],
                                                    [self.anisotropy_angle_x, self.anisotropy_angle_y,
                                                    self.anisotropy_angle_z]).T
  
          if style != 'masked':
              mask = np.zeros(npt, dtype='bool')
  
          xyz_points = np.concatenate((zpts[:, np.newaxis], ypts[:, np.newaxis],
                                       xpts[:, np.newaxis]), axis=1)
          xyz_data = np.concatenate((self.Z_ADJUSTED[:, np.newaxis],
                                     self.Y_ADJUSTED[:, np.newaxis],
                                     self.X_ADJUSTED[:, np.newaxis]), axis=1)
          bd = cdist(xyz_points, xyz_data, 'euclidean')
  
          if backend == 'vectorized':
              kvalues, sigmasq = self._exec_vector(a, bd, xyz_points, mask,
                                                   n_withdrifts, spec_drift_grids)
          elif backend == 'loop':
              kvalues, sigmasq = self._exec_loop(a, bd, xyz_points, mask,
                                                 n_withdrifts, spec_drift_grids)
          else:
              raise ValueError('Specified backend {} is not supported for '
                               '3D ordinary kriging.'.format(backend))
  
          if style == 'masked':
              kvalues = np.ma.array(kvalues, mask=mask)
              sigmasq = np.ma.array(sigmasq, mask=mask)
  
          if style in ['masked', 'grid']:
              kvalues = kvalues.reshape((nz, ny, nx))
              sigmasq = sigmasq.reshape((nz, ny, nx))
  
          return kvalues, sigmasq